This document contains a mathematics activity module for third grade. It includes goals, contents, and exercises on multiples, polygons, prime and composite numbers, algebraic expressions, and geometry topics. The goals are to understand the concepts of greatest common factor, identify different polygons, and recognize regular and irregular polygons. The contents covered are multiples and greatest common factor, regular and irregular polygons, prime and composite numbers, algebraic expressions, and the radius and diameter of a circle. The document contains several multi-step math word problems and exercises for students to complete.
Arithmetic to Analytic Geometry!
Before learning CALCULUS there are 10 points you need to reconsider as you continue your journey to the college life.
This exam offers word problems which includes branches like trigonometry, logarithms, functions, algebra, arithmetic and so forth. It ranges from 7th Grade to 10th Grade. It assess your basic knowledge of numbers and analytical skills. Hurry up and try!
1 Assignment #2 MAC 1140 – Spring 2020 – Due Apr.docxkarisariddell
1
Assignment #2
MAC 1140 – Spring 2020 – Due: April 7, 2020
1. We are given the polynomial 𝑓(𝑥) = 𝑥7 − 𝑥6 − 11𝑥5 + 11𝑥4 + 19𝑥3 − 19𝑥2 − 9𝑥 + 9.
(a) What is the degree of this polynomial? How many zeros does it have? Do these zeros have
to be real and/or distinct?
(b) What is the behavior of the polynomial as 𝑥 → +∞ and 𝑥 → −∞? Explain your answer.
(c) Describe, in your own words, the rational zero theorem. Taking into account the form of the
polynomial, can we use the rational zero theorem to find if the polynomial has rational
zeros? If yes, what are the possible zeros?
(d) Describe in your own words Descartes’ rule of signs. Using this rule, what is the possible
number of positive zeros of the polynomial, and what is the possible number of negative
zeros?
(e) Calculate the following values:
𝑓(−3) = ________ 𝑓(−2) = ________ 𝑓(−1) = ________ 𝑓(0) = ________
𝑓(1) = ________ 𝑓(2) = ________ 𝑓(3) = ________
𝑓(−4) = ________ 𝑓(4) = ________
2
(f) Describe in your own words the Factor Theorem. Using this theorem show that 𝑓(𝑥) =
(𝑥 + 3)(𝑥 + 1)(𝑥 − 1)(𝑥 − 3) ⋅ 𝑔(𝑥).
(g) Using long division, find 𝑔(𝑥). Show all your work.
(h) Calculate the following values:
𝑔(−1) = ________ 𝑔(1) = ________
(i) Using the Factor Theorem and synthetic division, factor 𝑔(𝑥). Show all your work.
(j) Describe the multiplicity of all the zeros of 𝑓(𝑥), and describe the behavior of the graph of
𝑓(𝑥) at these zeros (i.e., is the graph crossing the 𝑥-axis at these zeros or touches and turns
around?).
3
(k) What is the maximum number of turning points of 𝑓(𝑥)?
(l) Graph 𝑓(𝑥).
4
2. We are given the polynomial 𝑓(𝑥) = 4𝑥5 + 4𝑥4 + 𝑥3 − 2𝑥2 − 2𝑥 + 1.
(a) What is the degree of this polynomial? How many zeros does it have? Do these zeros have
to be real and/or distinct?
(b) What is the behavior of the polynomial as 𝑥 → +∞ and 𝑥 → −∞? Explain your answer.
(c) Describe, in your own words, the rational zero theorem. Taking into account the form of the
polynomial, can we use the rational zero theorem to find if the polynomial has rational
zeros? If yes, what are the possible zeros?
(d) Describe in your own words Descartes’ rule of signs. Using this rule, what is the possible
number of positive zeros of the polynomial, and what is the possible number of negative
zeros?
(e) Calculate the following values:
𝑓(−2) = ________ 𝑓(−1) = ________ 𝑓(0) = ________
𝑓(1) = ________ 𝑓(2) = ________
(f) Describe in your own words the Intermediate Value Theorem. Based on the results in (e)
above, and the possible rational zeros described in (c), show that 𝑥 −
1
2
is a factor of 𝑓(𝑥).
Clearly describe your reasoning.
5
(g) Describe in your own words the Factor Theorem. Using this theorem show that 𝑓(𝑥) =
(𝑥 + 1)(2𝑥 − 1) ⋅ 𝑔(𝑥
Arithmetic to Analytic Geometry!
Before learning CALCULUS there are 10 points you need to reconsider as you continue your journey to the college life.
This exam offers word problems which includes branches like trigonometry, logarithms, functions, algebra, arithmetic and so forth. It ranges from 7th Grade to 10th Grade. It assess your basic knowledge of numbers and analytical skills. Hurry up and try!
1 Assignment #2 MAC 1140 – Spring 2020 – Due Apr.docxkarisariddell
1
Assignment #2
MAC 1140 – Spring 2020 – Due: April 7, 2020
1. We are given the polynomial 𝑓(𝑥) = 𝑥7 − 𝑥6 − 11𝑥5 + 11𝑥4 + 19𝑥3 − 19𝑥2 − 9𝑥 + 9.
(a) What is the degree of this polynomial? How many zeros does it have? Do these zeros have
to be real and/or distinct?
(b) What is the behavior of the polynomial as 𝑥 → +∞ and 𝑥 → −∞? Explain your answer.
(c) Describe, in your own words, the rational zero theorem. Taking into account the form of the
polynomial, can we use the rational zero theorem to find if the polynomial has rational
zeros? If yes, what are the possible zeros?
(d) Describe in your own words Descartes’ rule of signs. Using this rule, what is the possible
number of positive zeros of the polynomial, and what is the possible number of negative
zeros?
(e) Calculate the following values:
𝑓(−3) = ________ 𝑓(−2) = ________ 𝑓(−1) = ________ 𝑓(0) = ________
𝑓(1) = ________ 𝑓(2) = ________ 𝑓(3) = ________
𝑓(−4) = ________ 𝑓(4) = ________
2
(f) Describe in your own words the Factor Theorem. Using this theorem show that 𝑓(𝑥) =
(𝑥 + 3)(𝑥 + 1)(𝑥 − 1)(𝑥 − 3) ⋅ 𝑔(𝑥).
(g) Using long division, find 𝑔(𝑥). Show all your work.
(h) Calculate the following values:
𝑔(−1) = ________ 𝑔(1) = ________
(i) Using the Factor Theorem and synthetic division, factor 𝑔(𝑥). Show all your work.
(j) Describe the multiplicity of all the zeros of 𝑓(𝑥), and describe the behavior of the graph of
𝑓(𝑥) at these zeros (i.e., is the graph crossing the 𝑥-axis at these zeros or touches and turns
around?).
3
(k) What is the maximum number of turning points of 𝑓(𝑥)?
(l) Graph 𝑓(𝑥).
4
2. We are given the polynomial 𝑓(𝑥) = 4𝑥5 + 4𝑥4 + 𝑥3 − 2𝑥2 − 2𝑥 + 1.
(a) What is the degree of this polynomial? How many zeros does it have? Do these zeros have
to be real and/or distinct?
(b) What is the behavior of the polynomial as 𝑥 → +∞ and 𝑥 → −∞? Explain your answer.
(c) Describe, in your own words, the rational zero theorem. Taking into account the form of the
polynomial, can we use the rational zero theorem to find if the polynomial has rational
zeros? If yes, what are the possible zeros?
(d) Describe in your own words Descartes’ rule of signs. Using this rule, what is the possible
number of positive zeros of the polynomial, and what is the possible number of negative
zeros?
(e) Calculate the following values:
𝑓(−2) = ________ 𝑓(−1) = ________ 𝑓(0) = ________
𝑓(1) = ________ 𝑓(2) = ________
(f) Describe in your own words the Intermediate Value Theorem. Based on the results in (e)
above, and the possible rational zeros described in (c), show that 𝑥 −
1
2
is a factor of 𝑓(𝑥).
Clearly describe your reasoning.
5
(g) Describe in your own words the Factor Theorem. Using this theorem show that 𝑓(𝑥) =
(𝑥 + 1)(2𝑥 − 1) ⋅ 𝑔(𝑥
More companies in the process of recruitment, play more emphasis in the topic of numbers in numerical aptitude. Especially for AMCAT aspirants this is very much useful.
Directions Please show all of your work for each problem. If app.docxduketjoy27252
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. The option of hand writing your work and scanning it is acceptable.
1. List all the factors of 88.
2. List all the prime numbers between 25 and 60.
3. Find the GCF for 16 and 17.
4. Find the LCM for 13 and 39.
5. Write the fraction in simplest form.
6. Multiply. Be sure to simplify the product.
7. Divide. Write the result in simplest form.
8. Add.
9. Perform the indicated operation. Write the result in simplest form. –
10. Perform the indicated operation. Write the result in simplest form. ÷
11. Find the decimal equivalent of rounded to the hundredths place.
12. Write 0.12 as a fraction and simplify.
13. Perform the indicated operation. 8.50 – 1.72
14. Divide.
15. Write 255% as a decimal.
16. Write 0.037 as a percent.
17. Evaluate. 56 ÷ 7 – 28 ÷ 7
18. Evaluate. 9 42
19. Multiply: (-1/4)(8/13)
20. Translate to an algebraic expression: Twice x, plus 5, is the same as -14.
21. Identify the property that is illustrated by the following statement. 5 + 15 = 15 + 5
22. Identify the property that is illustrated by the following statement.
(6 · 13) 10 = 6 · (13 · 10)
23. Identify the property that is illustrated by the following statement.
10 (3 + 11) = 10 3 + 10 11
24. Use the distributive property to remove the parentheses in the following expression. Then simplify your result where possible. 3.1(3 + 7)
25. Add. 14 + (–6)
26. Subtract. –17 – 6
27. Evaluate. 3 – (–3) – 13 – (–5)
28. Multiply.
29. Divide.
30. Evaluate. (–6)2 – 52
31. Evaluate. (–9)(0) + 13
32. A man lost 36 pounds (lb) while dieting. If he lost 3 pounds each week, how long has he been dieting?
33. Write the following phrase using symbols: 2 times the sum of v and p
34. Write the following phrase using symbols. Use the variable x to represent the number: The quotient of a number and 4
35. Dora puts 50 cents in her piggy bank every night before she goes to bed. If M represents the money (in dollars) in her piggy bank this morning, how much money (in dollars) is in her piggy bank when she goes to bed tonight?
36. Write the following geometric expression using the given symbols.
times the Area of the base (A) times the height(h)
37. Evaluate if x = 12, y = , and z = .
38. A formula that relates Fahrenheit and Celsius temperature is . If the current temperature is 59°F, what is the Celsius temperature?
39. If the circumference of a circle whose radius is r is given by C = 2πr, in which π ≈ 3.14, find the circumference when r = 15 meters (m).
40. Combine like terms: 9v + 6w + 4v
41. A rectangle has sides of 3x – 4 and 7x + 10. Provide a simplified expression for its perimeter.
42. Subtract 4ab3 from the sum of 10ab3 and 2ab3.
43. Use the distributive property to remove the p.
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
1. ACTIVIDAD DE MATEMÁTICAS
NOMBRE: FECHA
MULTIPLOS
MÓDULO DE REFORZAMIENTO
AÑO:2021 PERIODO: TERCERO
ÁREA: GRADO: DOCENTE:
Matemáticas 5 JORDY RODRIGUEZ RUIZ
LOGROS:
Comprender y aplicar el m.c.m. por los múltiplos comunes de los números.
Identifica adecuadamente los diferentes polígonos.
Reconoce los polígonos regulares e irregulares.
CONTENIDOS
Múltiplos y m.c.m.
Polígonos regulares e irregulares.
2. MINIMO COMUN MULTIPLO (m.c.m.)
POLIGONOS Y SUS ELEMENTOS
2. Mide los lados de cada polígono y calcula su perímetro.
3. Resuelve.
El perímetro de un cuadrado es 20 cm ¿cuánto mide cada lado?
Un campo tiene forma de pentágono y sus lados miden 12m, 9m, 10m, 7m y
5m
Le vamos a poner una valla alrededor
¿Cuántos metros de valla necesitamos?
4. ACTIVIDAD DE MATEMÁTICAS
NOMBRE: FECHA
1. Indica cuál de los siguientes números es primo (P) y cuál es compuesto (C), justifica
a) 37 ( ) b) 40 ( ) c) 20 ( ) d) 13 ( )
e) 15 ( ) f) 21 ( ) g) 99 ( ) h) 77 ( )
i) 88 ( ) j) 45 ( ) k) 46 ( ) l) 90 ( )
2. Responde si es verdadero (V) o falso (F), justifica tu respuesta
a) 60 es divisible por 2 ( )
b) 41 es divisible por 3 ( )
c) 22 es divisible por 4 ( )
d) 55 es divisible por 5 ( )
e) 28 es divisible por 8 ( )
f) 88 es divisible por 2 ( )
g) 85 es divisible por 5 ( )
h) 91 es divisible por 9 ( )
i) 99 es divisible por 11 ( )
j) 23 es divisible por 6 ( )
MÓDULO DE REFORZAMIENTO
AÑO:2021 PERIODO: TERCERO
ÁREA: GRADO: DOCENTE:
Matemáticas 6 JORDY RODRIGUEZ RUIZ
LOGROS:
Establece comparacionesentre cantidadesyexpresionesque involucranoperacionesyrelaciones
aditivasymultiplicativasysusrepresentacionesnuméricas
Conocerla formade cómo se calcula el áreade figurasgeométricas
Establecerdiferenciaentre áreayperímetrode figurasplanas.
CONTENIDOS
Númerosprimosynúmeroscompuestos
Figurasplanas
5. 3. ¿Un número compuesto es?
a) El que posee dos divisores exactamente
b) El que posee más de dos divisores
c) El que posee más de dos divisores, siendo el cero uno de ellos.
4. ¿Un numero primo es?
a) Todo aquel que solo tiene dos divisores: el mismo y la unidad.
b) Todo aquel que solo tiene dos divisores: el mismo y el cero.
c) Todo aquel que solo tiene dos divisores y el número 1, que solo tiene un
divisor.
5. ¿El numero 2 es?
a) Es compuesto porque es divisible por 2.
b) Es primo porque solo es divisible por el mismo y la unidad.
c) Es primo porque es el numero natural más pequeño y mayor que 1.
6. ¿Los múltiplos de un número primo?
a) Son más de dos
b) Son exactamente dos
c) Son infinitos.
7. ¿Los divisores de un número compuesto?
a) Son exactamente dos
b) Son al menos tres, siendo el 1 uno de ellos.
c) Son al menos tres, siendo el 0 uno de ellos.
8. ¿El producto de un número primo por uno compuesto es?
a) Compuesto, porque el numero resultante tendría todos los divisores del numero
compuesto, que son más de dos.
b) Compuesto, porque el numero resultante tendría todos los múltiplos del numero
compuesto, que son más de dos.
c) Primo, porque la propiedad de ser primo es más fuerte que la de ser compuesto.
9. ¿El numero 77 es?
a) Primo, porque 77= 7 * 11, o sea, solo tiene dos divisores.
b) Compuesto, porque al ser múltiplo de 7 y 11 tiene más de dos divisores.
c) Compuesto, porque al ser divisor de 7 y 11 tiene más de dos divisores.
6. FIGURAS PLANAS
1. Un rectángulo que mide 38 cm de largo por 21 cm de ancho. ¿Cuál es su área?
2. Un trapecio cuyas bases miden 12 y 15 cm y de altura 6 cm ¿Cuál es su área?
3. Un pentágono regular que mide 7.265 cm de lado y 5cm de apotema ¿Cuál es su
área?
4. Un hexágono regular de 3.46 cm de lado y 3 cm de apotema ¿Cuál es su área?
5. Si el área de un cuadrado es 81cm2 ¿Cuánto mide su lado?
7. 6. Un círculo cuyo diámetro mide 6cm hallar el área.
7. Un triángulo cuya base mide 9 cm y su altura 7 cm ¿Cuál es su área?
8. Calcula lo que costará sembrar césped en un jardín como el de la figura, si 1
m2 de césped plantado cuesta 100 euros.
9. Calcula:
a) La longitud de las diagonales de un rombo
inscrito en un rectángulo de 210 cm2 de área
y 30 cm de largo.
D =
d =
b) El área del rombo
A =
c) ¿Qué relación existe entre el área del
rectángulo y la del rombo inscrito en él?
8. ACTIVIDAD DE MATEMÁTICAS
NOMBRE: FECHA
1. Calcula las potencias de exponente par e impar:
a) 101 =
b) (–3)1
=
c) (–5)3
=
d) 103 =
e) (–12)2
=
f) (–4)4
=
g) (–4)5
=
h) (–12)3
=
i) 63 =
j) 204 =
MÓDULO DE REFORZAMIENTO
AÑO:2021 PERIODO: TERCERO
ÁREA: GRADO: DOCENTE:
Matemáticas 7 JORDY RODRIGUEZ RUIZ
LOGROS:
Aplicarlaspropiedadesde la potenciación endiferentesexpresionesaritméticasyalgebraicas.
Identificarpotenciasconigual base dentrode unaexpresiónaritméticaoalgebraica.
Resolverejerciciosyproblemasdel entornomediante laaplicacióndel teoremade Pitágoras.
Aplicary justificarcriteriosentre triángulosenlaresoluciónyformulaciónde problemas.
CONTENIDOS
Potenciación de números enteros
Propiedades de la potenciación
Teorema de Pitágoras
11. TEOREMA DE PITAGORAS
1. De la figura mostrada, calcular la longitud de la hipotenusa.
2. La hipotenusa de un triángulo mide √5 y uno de sus catetos mide 2m.
¿Cuánto mide el otro cateto?
3. ¿Cuánto mide la hipotenusa de un triángulo rectángulo cuyos catetos
miden 1m?
4. ¿A qué altura está la cometa de Ana si su cuerda mide 8 metros y tendría
que moverse 6 metros para situarse debajo de ella?
5. Una escalera de 10 m de longitud está apoyada sobre la pared. El pie de la
escalera dista 6 m de la pared. ¿Qué altura alcanza la escalera sobre la
pared?
12. ACTIVIDAD DE MATEMÁTICAS
NOMBRE: FECHA
1. Convertir los siguientes decimales exactos a fracción:
a) 0,2 b) 2,7 c) 0,25 d) 3,75 e) – 3,102 f) – 1,4238
g) 2,25 h) 10,85 i) 0,75 j) 9,78 k) 3,789 l) 2,345
2. Convertir los siguientes decimales periódicos puros a fracción
a) 5,2222… b) 2,717171… c) 3,141414… d) 0,156156…
e) 9,4444… f) 823,676767… g) 49,343434… h) 12,454545…
MÓDULO DE REFORZAMIENTO
AÑO:2021 PERIODO: TERCERO
ÁREA: GRADO: DOCENTE:
Matemáticas 8 JORDY RODRIGUEZ RUIZ
LOGROS:
Identificar un número decimal exacto de un número decimal periódico puro y periódico mixto.
Conocer adecuadamente los pasos para convertir decimal exacto y decimal periódico puro a
fracción.
Conocer las propiedades y las relaciones entre ángulos de un triángulo.
Realizar operaciones básicas con ángulos de triángulos.
CONTENIDOS
Convertir decimal exacto a fracción
Convertir decimal puro a fracción
Ángulos internos y externos de un triangulo
13. Interpreta
(Marca con una X)
3. Determina si cada número es racional o irracional.
4. Diga qué diferencia hay entre decimal finito y decimal periódico puro y de ejemplos.
Selección múltiple con única respuesta (marca con una X la respuesta correcta)
1. Es un numero decimal exacto:
a) 0,25 b) 3,1515… c) 12,4545… d) 3,141592…
2. Es un numero decimal periódico puro:
a) 0,75 b) 2,1515… c) 20,52525… d) 3,141592…
3. Es un numero decimal periódico mixto:
a) 20 ,52525… b) 3,141592… c) 2,1515… d) 0,25
4. Son potencias de 10:
a) 99, 999 b) 100, 1000 c) 99/10 d) todas las anteriores
5. Es un numero racional?
a) √2 b) √64 c) √3 d) ninguna de las anteriores
6. Es un numero irracional?:
a) √64 b) 3,14159265… c) 20 d) 15/3
7. El numero – 5 es:
a) Numero irracional b) Numero complejo
c) Numero racional d) numero natural
Número
Q
I
Decimal exacto Decimal periódico
Puro Mixto
43,98
7,659871…
√𝟓
14. ANGULOSINTERNOS Y EXTERNOS DE UN TRIANGULO
1. Encontrar el valor del ∢K
2. Encontrar el valor del ∢3
3. Encontrar el valor del ∢3
4. Encontrar el valor del ∢3
15. 5. Encontrar las medidas de: ∢A, ∢B, ∢2, ∢3
6. Mencione tres propiedades fundamentales de los triángulos.
7. ¿Cuál es la diferencia entre un triángulo cualquiera y un triángulo rectángulo?
8. Determina el valor de X, el ∢A, ∢B, ∢C
16. ACTIVIDAD DE MATEMÁTICAS
NOMBRE: FECHA
I. Hallar la adición y sustracción de las siguientes expresiones algebraicas
a) 12x + 5x =
b) 3x2 – 6x2 =
c) 13mn + (– 8mn) =
d) 3a + 5a +2b
e) 3x2y + (–5x2y)
f) 3x + (–5y) + (–6x) + (–2x) + x + 4y
g) x2 + x – 9 + 3x2 – 2x – 6
h) 3m2 +2mn – 5n2 + 4mn – 2n2 + m2 + 3mn – n2
i) ax + 3ax+2 + 5ax-1 + 6ax-3 + 7ax-3 – 2ax – 3ax+2
II. Hallar la multiplicación de las siguientes expresiones algebraicas
MÓDULO DE REFORZAMIENTO
AÑO:2021 PERIODO: TERCERO
ÁREA: GRADO: DOCENTE:
Matemáticas 9 JORDY RODRIGUEZ RUIZ
LOGROS:
- Utilizar las expresiones algebraicas y conocer el valor numérico de una expresión algebraica.
- Identificar monomios, polinomios y realizar sumas, restas, multiplicaciones y divisiones con ellos.
- Identificar la longitud de la circunferencia para hallar el radio o el diámetro de la misma.
CONTENIDOS
- Adición, sustracción, multiplicación y división de expresiones algebraicas
- Radio y diámetro de la circunferencia
17. a) (3x2) (4x4) =
b) (– 2y3) (3y4) =
c) (5xy2) (3x2y) =
d) (–3a2) (a2) =
e) (a) (–3a2b) (–ab3) =
f) 4x( x + 2) =
g) 2x( x – 1) =
h) 4x2 (x3 – 2) =
i) –2x2y3 (x3y6 + x4y3) =
III. Hallar la división de las siguientes expresiones algebraicas
a)
18𝑋4
6𝑋2
b)
25𝑎7
5𝑎5
c)
–36𝑥12
4𝑥8
d)
–30𝑎5𝑏12
6𝑎2𝑏8
IV. Diga qué diferencia hay entre las expresiones algebraicas monomio y polinomio.
V. Selección múltiple con única respuesta (marca con una X la
respuesta correcta)
1. Es una combinación de letras y números ligadas por los signos de las
operaciones:
b) Expresión polinómica b) expresión decimal c) expresión algebraica
c) d) expresión logarítmica
2. El perímetro y el área del siguiente triangulo están representados por
las expresiones:
a) P = m + n + h A = mn/2 b) P= m + n + h A = mn
c) P = m + n A = mn/2 d) P = m + n + h A = nh
e) f)
18. 3. Una expresión que representa en lenguaje algebraico la frase: "los
tres cuartos de un número" es:
a) X3/4 b) 3/4 b c) 4/3 y d) 3X4
4. La expresión algebraica que representa el área del
cuadrado es:
a) X b) 4X c) X2 d) 2X2
5. –2√2 – 1/2 √2 El símbolo que debe ir entre los
números es:
a) = b) > c) < d) ^
6. La expresión que representa el perímetro de la figura es:
a) y(y +2) b) y2
+ 2 c) 2y + 4 d) 4y +2
7. La expresión: "El cubo de un número menos un medio" se representa
como:
b) X3
– 1 b) X3
– X/2 c) X3
– X d) X3
– 1/2
d) Numero racional d) numero natural
RADIO Y DIAMETRO DE LA CIRCUNFERENCIA
1. Hallar el diámetro de una circunferencia que tiene 12m de longitud.
2. Hallar el radio de una circunferencia que tiene 10m de longitud.
3.
19. Hallar la longitud del arco de la circunferencia, con un radio de 3cm y un ángulo
central de 40°
4. Hallar la longitud del arco de la circunferencia, con un radio de 7cm y un ángulo
central de 110°
5. Diga cuál es la diferencia entre longitud de circunferencia y arco de la circunferencia.
6. Dibuja una circunferencia y señala el radio, el diámetro, el arco y el ángulo central.
7. Determina la longitud de arco de: